The present invention relates to well logging using electromagnetic measurements. More particularly, the invention relates to determining subsurface formation properties using electromagnetic induction tomography in a borehole lined with a conductive tubular or casing.
Geological formations forming a reservoir for the accumulation of hydrocarbons in the subsurface of the earth contain a network of interconnected paths in which fluids are disposed that may ingress or egress from the reservoir. To determine the behavior of the fluids in the aforementioned network, knowledge of both the porosity and permeability of the geological formations is desired. From this information, efficient development and management of hydrocarbon reservoirs may be achieved. For example, the resistivity of geological formations is a function of both porosity and permeability. Considering that hydrocarbons are electrically insulative and most water contains salts, which are highly conductive, resistivity measurements are a valuable tool to determine the presence of hydrocarbon reservoir in geological formations.
To that end, there have been many prior art attempts to model geological formations. In two articles, xe2x80x9cCrosshole Electromagnetic Tomography: A New Technology for Oil Field Characterization,xe2x80x9d The Leading Edge, March 1995, by Wilt et al. and xe2x80x9cCrosshole Electromagnetic Tomography: System Design Considerations and Field Results,xe2x80x9d Society of Exploration Geophysics, Vol. 60, No. 3 1995, by Wilt et al., measurement of geological formation resistivity is described employing a low frequency electromagnetic system.
FIG. 1 shows typical equipment used in the measurement of geological formation 10 resistivity between two drill holes 12a and 12b using electromagnetic induction. A transmitter T is located in one borehole, while a receiver R is placed in another borehole. The transmitter T typically consists of a coil (not shown) having a multi-turn loop (which consists of NT turns of wire) wrapped around a magnetically permeable core (mu-metal or ferrite) with a cross section, AT. The transmitter T may further comprise a capacitor (not shown) for tuning the frequency of the coil. When an alternating current, IT, at a frequency of f0 Hz passes through this multi-turn loop, a time varying magnetic moment, MT, is produced in the transmitter. This magnetic moment is defined as follows:
MT=NTITATxe2x80x83xe2x80x83(1)
The magnetic moment MT can be detected by the receiver R as a magnetic field, B0. The transmitter T, receiver R, or both are typically disposed in boreholes (e.g., 12a and 12b) in the earth formation 10. In this case, the detected magnetic field, B0, is proportional to the magnetic moment of the transmitter, MT, and to a geological factor, k1, as follows:
B0=k1MTxe2x80x83xe2x80x83(2)
The geological factor, k1, is a function of the spatial location and orientation of a field component of the magnetic field, B0, with respect to the magnetic moment of the transmitter, MT.
The receiver R typically includes one or more antennas (not shown). Each antenna includes a multi-turn loop of wire wound around a core of magnetically permeable metal or ferrite. The changing magnetic field sensed by the receiver R creates an induced voltage in the receiver coil (not shown). This induced voltage (VR) is a function of the detected magnetic field (BR), the frequency (f0), the number of turns (NR) of wire in the receiver coil, the effective cross-sectional area of the coil (AR), and the effective permeability (xcfx81R) of the coil. Thus, VR can be defined as follows:
VR=xcfx80f0BRNRARxcfx81Rxe2x80x83xe2x80x83(3)
While f0 and NR are known, the product, AR xcfx81R, is difficult to calculate. In practice, these constants may be grouped together as kR and equation (3) may be simplified as:
VR=kRBRxe2x80x83xe2x80x83(4)
where kR=xcfx80f0 NR AR xcfx81R. Thus, instead of determining the product AR xcfx81R, it is more convenient to determine kR according to the following procedures. First, the receiver coil is calibrated in a known field, at a known frequency. Then, the exact value for kR is derived from the magnetic field (BR) and the measured voltage (VR) according to the following equation:
kR=BR/VRxe2x80x83xe2x80x83(5)
When this system is placed in a conducting geological formation, the time-varying magnetic field, B0, which is produced by the transmitter magnetic moment, produces a voltage in the geological formation, which in turn drives a current therein, L1. The current, L1, is proportional to the conductivity of the geological formation and is generally concentric about the longitudinal axis of the borehole. The magnetic field proximate to the borehole results from a free space field, called the primary magnetic field, while the field resulting from current L1 is called the secondary magnetic field.
The current, L1, is typically out of phase with respect to the transmitter current, IT. At very low frequencies, where the inductive reactance is small, the current, L1, is proportional to dB/dt and is 90xc2x0 out of phase with respect to IT. As the frequency increases, the inductive reactance increases and the phase of the induced current, L1, increases to be greater than 90xc2x0. The secondary magnetic field induced by current L1 also has a phase shift relative to the induced current L1 and so the total magnetic field as detected by receiver R is complex.
The complex magnetic field detected by receiver R may be separated into two components: a real component, IR, which is in-phase with the transmitter current, IT, and an imaginary (or quadrature) component, II, which is phase-shifted by 90xc2x0. The values of the real component, IR, and the quadrature component, II, of the magnetic field at a given frequency and geometrical configuration uniquely specify the electrical resistivity of a homogeneous formation pierced by the drill holes. In an inhomogeneous geological formation, however, the complex field is measured at a succession of points along the longitudinal axis of the receiver borehole for each of a succession of transmitter locations. The multiplicity of measurements thus obtained can then be used to determine the inhomogeneous resistivity between the holes.
In both cases, i.e., measuring homogeneous geological formation resistivity or measuring inhomogeneous geological formation resistivity, the measurements are typically made before extraction of hydrocarbons takes place. This is because the boreholes typically are cased with conductive liners (e.g., metallic casing; see 16a and 16b in FIG. 1) in order to preserve the physical integrity of the borehole during hydrocarbon extraction. The conductive tubular liners interfere with resistivity measurements and are difficult and costly to remove from the borehole once they are installed. As a result, prior art systems such as that shown in FIG. 1 are not suitable for analyzing hydrocarbon reservoirs once extraction of the hydrocarbons begins.
The problems presented by conductive liners (16a and 16b in FIG. 1) are described by Augustin et al., in xe2x80x9cA Theoretical Study of Surface-to-Borehole Electromagnetic Logging in Cased Holes,xe2x80x9d Geophysics, Vol. 54, No. 1 (1989); Uchida et al., in xe2x80x9cEffect of a Steel Casing on Crosshole EM Measurements,xe2x80x9d SEG Annual Meeting, Texas (1991); and Wu et al., in xe2x80x9cInfluence of Steel Casing on Electromagnetic Signals,xe2x80x9d Geophysics, Vol. 59, No. 3 (1994). These prior art references show that coupling between a transmitter and a conductive liner is independent of the surrounding geological formation conductivity for a wide range of practical formation resistivities encountered in the field and that the magnetic field produced inside the conductive liner at a distance of a few meters or less from the transmitter depends only on the conductive liner properties and not on the formation properties.
The net or effective moment, Meff, of a transmitter inside a conductive liner is dictated by the inductive coupling between the transmitter and the conductive liner. Physically, the resistivity of the conductive liner is very low and the inductance relatively high. This property results in a current of almost the same magnitude as that of the transmitter current being induced in the conductive liner. Lenz""s Law predicts that the magnetic field generated by this induced current in the conductive liner will oppose the time-varying magnetic field produced by the transmitter current. Thus, the magnetic field generated by the transmitter is mostly cancelled out by the magnetic field generated by the conductive liner. As a result, the magnetic field external to the conductive liner is greatly reduced, and its magnitude is proportional to the difference in currents in the transmitter and the conductive liner. In effect, the conductive liner xe2x80x9cshieldsxe2x80x9d the transmitter from any receiver positioned outside of the conductive liner. An analogous situation is present with respect to a receiver if it is surrounded by a conductive liner, and the situation is exacerbated if both the transmitter and the receiver are surrounded by conductive liners.
To overcome the shielding problem, various techniques have been suggested. For example, U.S. Pat. No. 5,646,533, entitled xe2x80x9cInduction Measurement in the Presence of Metallic, Magnetic Wallsxe2x80x9d and issued to Locatelli, et al., discloses a method of magnetically saturating the metallic wall to overcome this problem. Alternatively, gapped casing has been used to achieve a similar effect. Another approach is to determine the conductive liner properties (e.g., radius, thickness, conductivity, and permeability) and then compensate for the these properties. However, the correction needed to compensate for the conductive liner properties may be several orders of magnitude larger than the magnetic field sensed by the receiver outside the casing. Any inaccurate correction for the conductive liner properties would have an enormous impact on the accuracy of the xe2x80x9ccorrected field.xe2x80x9d Furthermore, conductive liners often are not homogeneous (e.g., due to variation in thickness, corrosion, or rust formation); such variations may further compromise the accuracy of the xe2x80x9ccorrected field.xe2x80x9d For this reason, the prior art correction methods are not useful in practice.
It therefore is desirable to have better methods to overcome the effects of conductive liners so that dynamic measurements of the resistivity of geological formations while hydrocarbons are being extracted from reservoirs contained in the geological formations would be possible.
One aspect of the invention relates to electromagnetic tomography systems for determining properties of geological formation penetrated by at least one borehole lined with a conductive casing. One embodiment of the invention comprises a transmitter disposed in the cased borehole and adapted to induce a magnetic field, a first receiver disposed in the cased borehole in close proximity to the transmitter and adapted to detect the magnetic field induced in the conductive casing, and a second receiver adapted to detect the magnetic field induced in the geological formation. Another embodiment further comprises a second transmitter disposed in close proximity to the second receiver.
Another aspect of the invention relates to methods for determining a conductive casing correction constant for use in electromagnetic induction tomography in a borehole lined with a conductive casing. One method comprises generating a magnetic field inside a representative piece of the conductive casing; determining a first magnetic field amplitude inside the representative piece of the conductive casing at a location proximate to a position of the generating a magnetic field, determining a second magnetic field amplitude outside the representative piece of the conductive casing, and deriving the conductive casing correction constant from a ratio of the first magnetic field amplitude and the second magnetic field amplitude.
Yet another aspect of the invention relates to methods for determining properties of geological formation penetrated by at least one borehole lined with a conductive casing. One method comprises generating a magnetic field inside a representative piece of the conductive casing, determining a first magnetic field amplitude inside the representative piece of the conductive casing at a location proximity to a position of the generating a magnetic field, determining a second magnetic field amplitude outside the representative piece of the conductive casing, deriving a conductive casing correction constant from a ratio of the first magnetic field amplitude and the second magnetic field amplitude, generating a magnetic field in the formation from within a first borehole; measuring a reference magnetic field amplitude inside the first borehole; measuring a formation magnetic field amplitude in the geological formation; correcting the reference magnetic field amplitude and the formation magnetic field amplitude using the conductive casing correction constant, and deriving a formation property from the corrected reference magnetic field amplitude measurement and the corrected formation magnetic field amplitude measurement.
Other aspects of the invention will become apparent from the following discussion.